A fundamental differential system of Riemannian geometry

Abstract

We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree n associated to any given oriented Riemannian manifold M of dimension n + 1 . The framework is that of the tangent sphere bundle of M . We generalise to a Riemannian setting some results from the theory of hypersurfaces in flat Euclidean space. We give new applications and examples of the associated Euler–Lagrange differential systems.